TSTP Solution File: SEU208+2 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SEU208+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:02:39 EDT 2023
% Result : Theorem 64.42s 62.53s
% Output : Proof 64.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU208+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12 % Command : nanocop.sh %s %d
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu May 18 13:16:26 EDT 2023
% 0.12/0.33 % CPUTime :
% 64.42/62.53
% 64.42/62.53 /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 64.42/62.53 Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 64.42/62.53 %-----------------------------------------------------
% 64.42/62.53 ncf(matrix, plain, [(2815 ^ _61493) ^ [] : [2829 ^ _61493 : [(2832 ^ _61493) ^ [] : [-(in(ordered_pair(2809 ^ [], 2828 ^ []), 2811 ^ []))], (2834 ^ _61493) ^ [] : [-(in(2828 ^ [], 2810 ^ []))], (2836 ^ _61493) ^ [] : [in(2809 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []))], (2830 ^ _61493) ^ [] : [-(in(2828 ^ [], relation_rng(2811 ^ [])))]], 2816 ^ _61493 : [(2819 ^ _61493) ^ [_61566] : [in(_61566, relation_rng(2811 ^ [])), in(ordered_pair(2809 ^ [], _61566), 2811 ^ []), in(_61566, 2810 ^ [])], (2817 ^ _61493) ^ [] : [-(in(2809 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ [])))]]], (2813 ^ _61493) ^ [] : [-(relation(2811 ^ []))], !, (1603 ^ _17875) ^ [_43220, _43222] : [element(_43220, powerset(powerset(_43222))), -(element(complements_of_subsets(_43222, _43220), powerset(powerset(_43222))))], (1654 ^ _17875) ^ [] : [-(empty(empty_set))], (372 ^ _17875) ^ [_23265, _23267] : [relation(_23265), 375 ^ _17875 : [(376 ^ _17875) ^ [] : [_23265 = identity_relation(_23267), 379 ^ _17875 : [(388 ^ _17875) ^ [_23527, _23529] : [-(in(ordered_pair(_23529, _23527), _23265)), in(_23529, _23267), _23529 = _23527], (380 ^ _17875) ^ [_23418, _23420] : [in(ordered_pair(_23420, _23418), _23265), 383 ^ _17875 : [(386 ^ _17875) ^ [] : [-(_23420 = _23418)], (384 ^ _17875) ^ [] : [-(in(_23420, _23267))]]]]], (398 ^ _17875) ^ [] : [-(_23265 = identity_relation(_23267)), 411 ^ _17875 : [(416 ^ _17875) ^ [] : [in(ordered_pair(399 ^ [_23265, _23267], 400 ^ [_23265, _23267]), _23265)], (414 ^ _17875) ^ [] : [-(399 ^ [_23265, _23267] = 400 ^ [_23265, _23267])], (412 ^ _17875) ^ [] : [-(in(399 ^ [_23265, _23267], _23267))]], 403 ^ _17875 : [(406 ^ _17875) ^ [] : [in(399 ^ [_23265, _23267], _23267), 399 ^ [_23265, _23267] = 400 ^ [_23265, _23267]], (404 ^ _17875) ^ [] : [-(in(ordered_pair(399 ^ [_23265, _23267], 400 ^ [_23265, _23267]), _23265))]]]]], (150 ^ _17875) ^ [_19942, _19944, _19946, _19948] : [-(cartesian_product2(_19948, _19944) = cartesian_product2(_19946, _19942)), _19948 = _19946, _19944 = _19942], (1953 ^ _17875) ^ [_47883, _47885, _47887, _47889] : [-(in(ordered_pair(_47889, _47887), cartesian_product2(_47885, _47883))), in(_47889, _47885), in(_47887, _47883)], (252 ^ _17875) ^ [_21461, _21463, _21465, _21467] : [-(set_intersection2(_21467, _21463) = set_intersection2(_21465, _21461)), _21467 = _21465, _21463 = _21461], (895 ^ _17875) ^ [_31926, _31928, _31930] : [-(_31926 = unordered_pair(_31930, _31928)), 899 ^ _17875 : [(904 ^ _17875) ^ [] : [896 ^ [_31926, _31928, _31930] = _31928], (902 ^ _17875) ^ [] : [896 ^ [_31926, _31928, _31930] = _31930], (900 ^ _17875) ^ [] : [-(in(896 ^ [_31926, _31928, _31930], _31926))]], 905 ^ _17875 : [(906 ^ _17875) ^ [] : [-(896 ^ [_31926, _31928, _31930] = _31930), -(896 ^ [_31926, _31928, _31930] = _31928)], (912 ^ _17875) ^ [] : [in(896 ^ [_31926, _31928, _31930], _31926)]]], (2600 ^ _17875) ^ [_57147] : [relation(_57147), 2603 ^ _17875 : [(2610 ^ _17875) ^ [] : [relation_rng(_57147) = empty_set, -(relation_dom(_57147) = empty_set)], (2604 ^ _17875) ^ [] : [relation_dom(_57147) = empty_set, -(relation_rng(_57147) = empty_set)]]], (801 ^ _17875) ^ [_30493] : [relation(_30493), 804 ^ _17875 : [(805 ^ _17875) ^ [_30579] : [relation(_30579), 808 ^ _17875 : [(809 ^ _17875) ^ [] : [_30493 = _30579, 812 ^ _17875 : [(819 ^ _17875) ^ [_30814, _30816] : [in(ordered_pair(_30816, _30814), _30579), -(in(ordered_pair(_30816, _30814), _30493))], (813 ^ _17875) ^ [_30725, _30727] : [in(ordered_pair(_30727, _30725), _30493), -(in(ordered_pair(_30727, _30725), _30579))]]], (825 ^ _17875) ^ [] : [-(_30493 = _30579), 830 ^ _17875 : [(833 ^ _17875) ^ [] : [in(ordered_pair(826 ^ [_30493, _30579], 827 ^ [_30493, _30579]), _30579)], (831 ^ _17875) ^ [] : [-(in(ordered_pair(826 ^ [_30493, _30579], 827 ^ [_30493, _30579]), _30493))]], 834 ^ _17875 : [(837 ^ _17875) ^ [] : [in(ordered_pair(826 ^ [_30493, _30579], 827 ^ [_30493, _30579]), _30493)], (835 ^ _17875) ^ [] : [-(in(ordered_pair(826 ^ [_30493, _30579], 827 ^ [_30493, _30579]), _30579))]]]]]]], (1503 ^ _17875) ^ [] : [true___, -(true___)], (1278 ^ _17875) ^ [_38328, _38330] : [-(ordered_pair(_38330, _38328) = unordered_pair(unordered_pair(_38330, _38328), singleton(_38330)))], (1790 ^ _17875) ^ [_45629, _45631] : [subset(singleton(_45631), _45629), -(in(_45631, _45629))], (2340 ^ _17875) ^ [_53525] : [-(set_difference(_53525, empty_set) = _53525)], (1866 ^ _17875) ^ [_46671, _46673, _46675, _46677] : [-(in(ordered_pair(_46677, _46675), cartesian_product2(_46673, _46671))), in(_46677, _46673), in(_46675, _46671)], (1670 ^ _17875) ^ [_44083, _44085] : [-(empty(_44085)), empty(set_union2(_44085, _44083))], (278 ^ _17875) ^ [_21844, _21846] : [_21846 = _21844, -(identity_relation(_21846) = identity_relation(_21844))], (2457 ^ _17875) ^ [_55246] : [relation(_55246), 2460 ^ _17875 : [(2461 ^ _17875) ^ [_55321] : [relation(_55321), subset(relation_dom(_55246), relation_rng(_55321)), -(relation_rng(relation_composition(_55321, _55246)) = relation_rng(_55246))]]], (1192 ^ _17875) ^ [_36870, _36872, _36874] : [_36870 = set_difference(_36874, _36872), 1195 ^ _17875 : [(1204 ^ _17875) ^ [_37072] : [-(in(_37072, _36870)), in(_37072, _36874), -(in(_37072, _36872))], (1196 ^ _17875) ^ [_36961] : [in(_36961, _36870), 1199 ^ _17875 : [(1202 ^ _17875) ^ [] : [in(_36961, _36872)], (1200 ^ _17875) ^ [] : [-(in(_36961, _36874))]]]]], (2630 ^ _17875) ^ [_57526] : [empty(_57526), -(_57526 = empty_set)], (206 ^ _17875) ^ [_20780, _20782] : [_20782 = _20780, -(cast_to_subset(_20782) = cast_to_subset(_20780))], (1108 ^ _17875) ^ [_35432] : [relation(_35432), 1111 ^ _17875 : [(1112 ^ _17875) ^ [_35524] : [_35524 = relation_dom(_35432), 1115 ^ _17875 : [(1123 ^ _17875) ^ [_35706] : [1124 ^ _17875 : [(1125 ^ _17875) ^ [_35750] : [in(ordered_pair(_35706, _35750), _35432)]], -(in(_35706, _35524))], (1116 ^ _17875) ^ [_35611] : [in(_35611, _35524), -(in(ordered_pair(_35611, 1119 ^ [_35432, _35524, _35611]), _35432))]]], (1129 ^ _17875) ^ [_35806] : [-(_35806 = relation_dom(_35432)), 1133 ^ _17875 : [(1136 ^ _17875) ^ [_35940] : [in(ordered_pair(1130 ^ [_35432, _35806], _35940), _35432)], (1134 ^ _17875) ^ [] : [-(in(1130 ^ [_35432, _35806], _35806))]], 1138 ^ _17875 : [(1141 ^ _17875) ^ [] : [in(1130 ^ [_35432, _35806], _35806)], (1139 ^ _17875) ^ [] : [-(in(ordered_pair(1130 ^ [_35432, _35806], 1137 ^ [_35432, _35806]), _35432))]]]]], (2588 ^ _17875) ^ [_56978] : [relation(_56978), 2593 ^ _17875 : [(2596 ^ _17875) ^ [] : [relation_rng(_56978) = empty_set], (2594 ^ _17875) ^ [] : [relation_dom(_56978) = empty_set]], -(_56978 = empty_set)], (34 ^ _17875) ^ [_18328, _18330, _18332, _18334] : [-(proper_subset(_18332, _18328)), proper_subset(_18334, _18330), _18334 = _18332, _18330 = _18328], (2668 ^ _17875) ^ [_58061, _58063] : [in(_58063, _58061), empty(_58061)], (1688 ^ _17875) ^ [_44311, _44313] : [empty(cartesian_product2(_44313, _44311)), -(empty(_44313)), -(empty(_44311))], (1756 ^ _17875) ^ [_45164] : [relation(_45164), -(relation_inverse(relation_inverse(_45164)) = _45164)], (2013 ^ _17875) ^ [_48705, _48707, _48709] : [subset(_48709, _48707), 2016 ^ _17875 : [(2019 ^ _17875) ^ [] : [-(subset(cartesian_product2(_48705, _48709), cartesian_product2(_48705, _48707)))], (2017 ^ _17875) ^ [] : [-(subset(cartesian_product2(_48709, _48705), cartesian_product2(_48707, _48705)))]]], (1963 ^ _17875) ^ [_48034, _48036, _48038, _48040] : [unordered_pair(_48040, _48038) = unordered_pair(_48036, _48034), -(_48040 = _48036), -(_48040 = _48034)], (1784 ^ _17875) ^ [_45576, _45578] : [-(in(_45578, _45576)), -(disjoint(singleton(_45578), _45576))], (1770 ^ _17875) ^ [_45388] : [singleton(_45388) = empty_set], (2518 ^ _17875) ^ [_56075] : [-(_56075 = empty_set), 2521 ^ _17875 : [(2522 ^ _17875) ^ [_56158] : [element(_56158, powerset(_56075)), 2525 ^ _17875 : [(2526 ^ _17875) ^ [_56236] : [element(_56236, _56075), -(in(_56236, _56158)), -(in(_56236, subset_complement(_56075, _56158)))]]]]], (2167 ^ _17875) ^ [_51049, _51051, _51053] : [relation(_51049), in(ordered_pair(_51053, _51051), _51049), 2174 ^ _17875 : [(2177 ^ _17875) ^ [] : [-(in(_51051, relation_rng(_51049)))], (2175 ^ _17875) ^ [] : [-(in(_51053, relation_dom(_51049)))]]], (182 ^ _17875) ^ [_20410, _20412, _20414, _20416] : [-(complements_of_subsets(_20416, _20412) = complements_of_subsets(_20414, _20410)), _20416 = _20414, _20412 = _20410], (1477 ^ _17875) ^ [] : [true___, -(true___)], (1235 ^ _17875) ^ [_37580] : [relation(_37580), 1238 ^ _17875 : [(1239 ^ _17875) ^ [_37672] : [_37672 = relation_rng(_37580), 1242 ^ _17875 : [(1250 ^ _17875) ^ [_37854] : [1251 ^ _17875 : [(1252 ^ _17875) ^ [_37898] : [in(ordered_pair(_37898, _37854), _37580)]], -(in(_37854, _37672))], (1243 ^ _17875) ^ [_37759] : [in(_37759, _37672), -(in(ordered_pair(1246 ^ [_37580, _37672, _37759], _37759), _37580))]]], (1256 ^ _17875) ^ [_37954] : [-(_37954 = relation_rng(_37580)), 1260 ^ _17875 : [(1263 ^ _17875) ^ [_38088] : [in(ordered_pair(_38088, 1257 ^ [_37580, _37954]), _37580)], (1261 ^ _17875) ^ [] : [-(in(1257 ^ [_37580, _37954], _37954))]], 1265 ^ _17875 : [(1268 ^ _17875) ^ [] : [in(1257 ^ [_37580, _37954], _37954)], (1266 ^ _17875) ^ [] : [-(in(ordered_pair(1264 ^ [_37580, _37954], 1257 ^ [_37580, _37954]), _37580))]]]]], (2421 ^ _17875) ^ [_54695, _54697] : [subset(_54697, _54695), -(_54695 = set_union2(_54697, set_difference(_54695, _54697)))], (2290 ^ _17875) ^ [_52831, _52833] : [subset(singleton(_52833), _52831), -(in(_52833, _52831))], (1280 ^ _17875) ^ [_38364] : [relation(_38364), -(relation_field(_38364) = set_union2(relation_dom(_38364), relation_rng(_38364)))], (2451 ^ _17875) ^ [_55159, _55161] : [in(_55161, _55159), -(set_union2(singleton(_55161), _55159) = _55159)], (2760 ^ _17875) ^ [_59351, _59353] : [relation(_59351), -(subset(relation_rng(relation_dom_restriction(_59351, _59353)), relation_rng(_59351)))], (322 ^ _17875) ^ [_22482, _22484, _22486, _22488] : [-(relation_inverse_image(_22488, _22484) = relation_inverse_image(_22486, _22482)), _22488 = _22486, _22484 = _22482], (2769 ^ _17875) ^ [_59575] : [-(in(_59575, 2767 ^ [_59575]))], (1509 ^ _17875) ^ [] : [true___, -(true___)], (1921 ^ _17875) ^ [_47395, _47397] : [element(_47395, powerset(powerset(_47397))), -(meet_of_subsets(_47397, _47395) = set_meet(_47395))], (438 ^ _17875) ^ [_24284] : [relation(_24284), 441 ^ _17875 : [(442 ^ _17875) ^ [_24384, _24386] : [relation(_24384), 445 ^ _17875 : [(446 ^ _17875) ^ [] : [_24384 = relation_dom_restriction(_24284, _24386), 449 ^ _17875 : [(458 ^ _17875) ^ [_24663, _24665] : [-(in(ordered_pair(_24665, _24663), _24384)), in(_24665, _24386), in(ordered_pair(_24665, _24663), _24284)], (450 ^ _17875) ^ [_24546, _24548] : [in(ordered_pair(_24548, _24546), _24384), 453 ^ _17875 : [(456 ^ _17875) ^ [] : [-(in(ordered_pair(_24548, _24546), _24284))], (454 ^ _17875) ^ [] : [-(in(_24548, _24386))]]]]], (468 ^ _17875) ^ [] : [-(_24384 = relation_dom_restriction(_24284, _24386)), 481 ^ _17875 : [(486 ^ _17875) ^ [] : [in(ordered_pair(469 ^ [_24284, _24384, _24386], 470 ^ [_24284, _24384, _24386]), _24384)], (484 ^ _17875) ^ [] : [-(in(ordered_pair(469 ^ [_24284, _24384, _24386], 470 ^ [_24284, _24384, _24386]), _24284))], (482 ^ _17875) ^ [] : [-(in(469 ^ [_24284, _24384, _24386], _24386))]], 473 ^ _17875 : [(476 ^ _17875) ^ [] : [in(469 ^ [_24284, _24384, _24386], _24386), in(ordered_pair(469 ^ [_24284, _24384, _24386], 470 ^ [_24284, _24384, _24386]), _24284)], (474 ^ _17875) ^ [] : [-(in(ordered_pair(469 ^ [_24284, _24384, _24386], 470 ^ [_24284, _24384, _24386]), _24384))]]]]]]], (1903 ^ _17875) ^ [] : [empty(1901 ^ [])], (1489 ^ _17875) ^ [] : [true___, -(true___)], (1684 ^ _17875) ^ [] : [-(empty(empty_set))], (2636 ^ _17875) ^ [_57599, _57601] : [subset(singleton(_57601), singleton(_57599)), -(_57601 = _57599)], (2771 ^ _17875) ^ [_59603, _59605, _59607] : [-(in(_59603, 2767 ^ [_59607])), in(_59605, 2767 ^ [_59607]), subset(_59603, _59605)], (2781 ^ _17875) ^ [_59756, _59758] : [in(_59756, 2767 ^ [_59758]), 2785 ^ _17875 : [(2788 ^ _17875) ^ [_59902] : [subset(_59902, _59756), -(in(_59902, 2784 ^ [_59756, _59758]))], (2786 ^ _17875) ^ [] : [-(in(2784 ^ [_59756, _59758], 2767 ^ [_59758]))]]], (1768 ^ _17875) ^ [_45354, _45356] : [proper_subset(_45356, _45356)], (1750 ^ _17875) ^ [_45071, _45073] : [element(_45071, powerset(_45073)), -(subset_complement(_45073, subset_complement(_45073, _45071)) = _45071)], (2165 ^ _17875) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (242 ^ _17875) ^ [_21312, _21314, _21316, _21318] : [-(set_union2(_21318, _21314) = set_union2(_21316, _21312)), _21318 = _21316, _21314 = _21312], (1332 ^ _17875) ^ [_39260, _39262] : [set_intersection2(_39262, _39260) = empty_set, -(disjoint(_39262, _39260))], (989 ^ _17875) ^ [_33439, _33441, _33443] : [-(_33439 = cartesian_product2(_33443, _33441)), 1007 ^ _17875 : [(1010 ^ _17875) ^ [] : [-(in(1006 ^ [_33439, _33441, _33443], _33441))], (1012 ^ _17875) ^ [] : [-(990 ^ [_33439, _33441, _33443] = ordered_pair(1005 ^ [_33439, _33441, _33443], 1006 ^ [_33439, _33441, _33443]))], (1014 ^ _17875) ^ [] : [in(990 ^ [_33439, _33441, _33443], _33439)], (1008 ^ _17875) ^ [] : [-(in(1005 ^ [_33439, _33441, _33443], _33443))]], 993 ^ _17875 : [(996 ^ _17875) ^ [_33609, _33611] : [in(_33611, _33443), in(_33609, _33441), 990 ^ [_33439, _33441, _33443] = ordered_pair(_33611, _33609)], (994 ^ _17875) ^ [] : [-(in(990 ^ [_33439, _33441, _33443], _33439))]]], (2726 ^ _17875) ^ [_58856, _58858, _58860] : [-(subset(set_union2(_58860, _58856), _58858)), subset(_58860, _58858), subset(_58856, _58858)], (841 ^ _17875) ^ [_31204, _31206] : [-(empty(_31206)), 844 ^ _17875 : [(851 ^ _17875) ^ [] : [in(_31204, _31206), -(element(_31204, _31206))], (845 ^ _17875) ^ [] : [element(_31204, _31206), -(in(_31204, _31206))]]], (542 ^ _17875) ^ [_26170] : [relation(_26170), 545 ^ _17875 : [(546 ^ _17875) ^ [_26277, _26279] : [_26277 = relation_image(_26170, _26279), 549 ^ _17875 : [(559 ^ _17875) ^ [_26510] : [-(in(_26510, _26277)), 560 ^ _17875 : [(561 ^ _17875) ^ [_26557] : [in(ordered_pair(_26557, _26510), _26170), in(_26557, _26279)]]], (550 ^ _17875) ^ [_26374] : [in(_26374, _26277), 554 ^ _17875 : [(557 ^ _17875) ^ [] : [-(in(553 ^ [_26170, _26277, _26279, _26374], _26279))], (555 ^ _17875) ^ [] : [-(in(ordered_pair(553 ^ [_26170, _26277, _26279, _26374], _26374), _26170))]]]]], (569 ^ _17875) ^ [_26675, _26677] : [-(_26675 = relation_image(_26170, _26677)), 582 ^ _17875 : [(587 ^ _17875) ^ [] : [in(570 ^ [_26170, _26675, _26677], _26675)], (585 ^ _17875) ^ [] : [-(in(581 ^ [_26170, _26675, _26677], _26677))], (583 ^ _17875) ^ [] : [-(in(ordered_pair(581 ^ [_26170, _26675, _26677], 570 ^ [_26170, _26675, _26677]), _26170))]], 573 ^ _17875 : [(576 ^ _17875) ^ [_26823] : [in(ordered_pair(_26823, 570 ^ [_26170, _26675, _26677]), _26170), in(_26823, _26677)], (574 ^ _17875) ^ [] : [-(in(570 ^ [_26170, _26675, _26677], _26675))]]]]], (2113 ^ _17875) ^ [_50277, _50279] : [relation(_50277), -(relation_image(_50277, _50279) = relation_image(_50277, set_intersection2(relation_dom(_50277), _50279)))], (2794 ^ _17875) ^ [_59997, _59999] : [subset(_59997, 2767 ^ [_59999]), -(are_equipotent(_59997, 2767 ^ [_59999])), -(in(_59997, 2767 ^ [_59999]))], (2201 ^ _17875) ^ [_51558, _51560, _51562] : [subset(_51562, _51560), -(subset(set_intersection2(_51562, _51558), set_intersection2(_51560, _51558)))], (1927 ^ _17875) ^ [_47490, _47492, _47494] : [-(subset_difference(_47494, _47492, _47490) = set_difference(_47492, _47490)), element(_47492, powerset(_47494)), element(_47490, powerset(_47494))], (1483 ^ _17875) ^ [] : [true___, -(true___)], (1676 ^ _17875) ^ [_44174, _44176] : [empty(unordered_pair(_44176, _44174))], (1621 ^ _17875) ^ [] : [true___, -(true___)], (48 ^ _17875) ^ [_18521, _18523, _18525, _18527] : [-(disjoint(_18525, _18521)), disjoint(_18527, _18523), _18527 = _18525, _18523 = _18521], (1900 ^ _17875) ^ [] : [-(empty(1898 ^ []))], (1973 ^ _17875) ^ [_48144, _48146, _48148] : [relation(_48144), 1976 ^ _17875 : [(1985 ^ _17875) ^ [] : [-(in(_48148, relation_rng(relation_rng_restriction(_48146, _48144)))), in(_48148, _48146), in(_48148, relation_rng(_48144))], (1977 ^ _17875) ^ [] : [in(_48148, relation_rng(relation_rng_restriction(_48146, _48144))), 1980 ^ _17875 : [(1983 ^ _17875) ^ [] : [-(in(_48148, relation_rng(_48144)))], (1981 ^ _17875) ^ [] : [-(in(_48148, _48146))]]]]], (284 ^ _17875) ^ [_21929, _21931, _21933, _21935] : [-(relation_dom_restriction(_21935, _21931) = relation_dom_restriction(_21933, _21929)), _21935 = _21933, _21931 = _21929], (1778 ^ _17875) ^ [_45500, _45502] : [disjoint(singleton(_45502), _45500), in(_45502, _45500)], (2381 ^ _17875) ^ [_54071, _54073] : [element(_54071, powerset(_54073)), 2384 ^ _17875 : [(2385 ^ _17875) ^ [_54149] : [element(_54149, powerset(_54073)), 2388 ^ _17875 : [(2395 ^ _17875) ^ [] : [subset(_54071, subset_complement(_54073, _54149)), -(disjoint(_54071, _54149))], (2389 ^ _17875) ^ [] : [disjoint(_54071, _54149), -(subset(_54071, subset_complement(_54073, _54149)))]]]]], (1915 ^ _17875) ^ [_47300, _47302] : [element(_47300, powerset(powerset(_47302))), -(union_of_subsets(_47302, _47300) = union(_47300))], (1726 ^ _17875) ^ [_44753] : [empty(_44753), 1729 ^ _17875 : [(1732 ^ _17875) ^ [] : [-(relation(relation_rng(_44753)))], (1730 ^ _17875) ^ [] : [-(empty(relation_rng(_44753)))]]], (192 ^ _17875) ^ [_20559, _20561, _20563, _20565, _20567, _20569] : [-(subset_difference(_20569, _20565, _20561) = subset_difference(_20567, _20563, _20559)), _20569 = _20567, _20565 = _20563, _20561 = _20559], (160 ^ _17875) ^ [_20091, _20093] : [_20093 = _20091, -(relation_field(_20093) = relation_field(_20091))], (2411 ^ _17875) ^ [_54537] : [relation(_54537), 2414 ^ _17875 : [(2415 ^ _17875) ^ [_54602] : [relation(_54602), -(subset(relation_rng(relation_composition(_54537, _54602)), relation_rng(_54602)))]]], (1018 ^ _17875) ^ [_33957] : [relation(_33957), 1021 ^ _17875 : [(1022 ^ _17875) ^ [_34043] : [relation(_34043), 1025 ^ _17875 : [(1026 ^ _17875) ^ [] : [subset(_33957, _34043), 1029 ^ _17875 : [(1030 ^ _17875) ^ [_34174, _34176] : [in(ordered_pair(_34176, _34174), _33957), -(in(ordered_pair(_34176, _34174), _34043))]]], (1036 ^ _17875) ^ [] : [1039 ^ _17875 : [(1042 ^ _17875) ^ [] : [in(ordered_pair(1037 ^ [_33957, _34043], 1038 ^ [_33957, _34043]), _34043)], (1040 ^ _17875) ^ [] : [-(in(ordered_pair(1037 ^ [_33957, _34043], 1038 ^ [_33957, _34043]), _33957))]], -(subset(_33957, _34043))]]]]], (2270 ^ _17875) ^ [_52514] : [relation(_52514), 2273 ^ _17875 : [(2276 ^ _17875) ^ [] : [-(relation_dom(_52514) = relation_rng(relation_inverse(_52514)))], (2274 ^ _17875) ^ [] : [-(relation_rng(_52514) = relation_dom(relation_inverse(_52514)))]]], (72 ^ _17875) ^ [_18839, _18841, _18843, _18845] : [-(subset(_18843, _18839)), subset(_18845, _18841), _18845 = _18843, _18841 = _18839], (20 ^ _17875) ^ [_18135, _18137, _18139, _18141] : [-(element(_18139, _18135)), element(_18141, _18137), _18141 = _18139, _18137 = _18135], (124 ^ _17875) ^ [_19559, _19561] : [_19561 = _19559, -(set_meet(_19561) = set_meet(_19559))], (1396 ^ _17875) ^ [_40529, _40531] : [element(_40529, powerset(powerset(_40531))), 1399 ^ _17875 : [(1400 ^ _17875) ^ [_40635] : [element(_40635, powerset(powerset(_40531))), 1403 ^ _17875 : [(1404 ^ _17875) ^ [] : [_40635 = complements_of_subsets(_40531, _40529), 1407 ^ _17875 : [(1408 ^ _17875) ^ [_40786] : [element(_40786, powerset(_40531)), 1411 ^ _17875 : [(1418 ^ _17875) ^ [] : [in(subset_complement(_40531, _40786), _40529), -(in(_40786, _40635))], (1412 ^ _17875) ^ [] : [in(_40786, _40635), -(in(subset_complement(_40531, _40786), _40529))]]]]], (1424 ^ _17875) ^ [] : [-(_40635 = complements_of_subsets(_40531, _40529)), 1426 ^ _17875 : [(1429 ^ _17875) ^ [] : [1430 ^ _17875 : [(1433 ^ _17875) ^ [] : [in(subset_complement(_40531, 1425 ^ [_40529, _40531, _40635]), _40529)], (1431 ^ _17875) ^ [] : [-(in(1425 ^ [_40529, _40531, _40635], _40635))]], 1434 ^ _17875 : [(1437 ^ _17875) ^ [] : [in(1425 ^ [_40529, _40531, _40635], _40635)], (1435 ^ _17875) ^ [] : [-(in(subset_complement(_40531, 1425 ^ [_40529, _40531, _40635]), _40529))]]], (1427 ^ _17875) ^ [] : [-(element(1425 ^ [_40529, _40531, _40635], powerset(_40531)))]]]]]]], (222 ^ _17875) ^ [_21014, _21016, _21018, _21020] : [-(subset_complement(_21020, _21016) = subset_complement(_21018, _21014)), _21020 = _21018, _21016 = _21014], (2481 ^ _17875) ^ [_55604, _55606] : [element(_55604, powerset(powerset(_55606))), -(_55604 = empty_set), -(union_of_subsets(_55606, complements_of_subsets(_55606, _55604)) = subset_difference(_55606, cast_to_subset(_55606), meet_of_subsets(_55606, _55604)))], (1656 ^ _17875) ^ [_43895, _43897] : [empty(ordered_pair(_43897, _43895))], (2254 ^ _17875) ^ [_52276, _52278, _52280] : [subset(_52280, _52278), -(subset(set_difference(_52280, _52276), set_difference(_52278, _52276)))], (726 ^ _17875) ^ [_29389, _29391] : [_29389 = singleton(_29391), 729 ^ _17875 : [(736 ^ _17875) ^ [_29543] : [_29543 = _29391, -(in(_29543, _29389))], (730 ^ _17875) ^ [_29468] : [in(_29468, _29389), -(_29468 = _29391)]]], (2260 ^ _17875) ^ [_52367, _52369, _52371, _52373] : [ordered_pair(_52373, _52371) = ordered_pair(_52369, _52367), 2263 ^ _17875 : [(2266 ^ _17875) ^ [] : [-(_52371 = _52367)], (2264 ^ _17875) ^ [] : [-(_52373 = _52369)]]], (2 ^ _17875) ^ [_17902] : [-(_17902 = _17902)], (1449 ^ _17875) ^ [_41433, _41435] : [-(proper_subset(_41435, _41433)), subset(_41435, _41433), -(_41435 = _41433)], (873 ^ _17875) ^ [_31626, _31628, _31630] : [_31626 = unordered_pair(_31630, _31628), 876 ^ _17875 : [(877 ^ _17875) ^ [_31715] : [in(_31715, _31626), -(_31715 = _31630), -(_31715 = _31628)], (887 ^ _17875) ^ [_31805] : [888 ^ _17875 : [(891 ^ _17875) ^ [] : [_31805 = _31628], (889 ^ _17875) ^ [] : [_31805 = _31630]], -(in(_31805, _31626))]]], (2240 ^ _17875) ^ [_52082] : [-(subset(empty_set, _52082))], (1587 ^ _17875) ^ [_42988, _42990, _42992] : [-(element(subset_difference(_42992, _42990, _42988), powerset(_42992))), element(_42990, powerset(_42992)), element(_42988, powerset(_42992))], (2021 ^ _17875) ^ [_48834, _48836] : [relation(_48834), -(relation_rng(relation_rng_restriction(_48836, _48834)) = set_intersection2(relation_rng(_48834), _48836))], (2320 ^ _17875) ^ [_53257, _53259] : [-(set_union2(_53259, set_difference(_53257, _53259)) = set_union2(_53259, _53257))], (2207 ^ _17875) ^ [_51649, _51651] : [subset(_51651, _51649), -(set_intersection2(_51651, _51649) = _51651)], (2185 ^ _17875) ^ [_51307] : [relation(_51307), 2188 ^ _17875 : [(2189 ^ _17875) ^ [_51385] : [relation(_51385), subset(_51307, _51385), 2196 ^ _17875 : [(2199 ^ _17875) ^ [] : [-(subset(relation_rng(_51307), relation_rng(_51385)))], (2197 ^ _17875) ^ [] : [-(subset(relation_dom(_51307), relation_dom(_51385)))]]]]], (428 ^ _17875) ^ [_24153, _24155] : [-(_24155 = _24153), subset(_24155, _24153), subset(_24153, _24155)], (354 ^ _17875) ^ [_23023, _23025] : [proper_subset(_23025, _23023), proper_subset(_23023, _23025)], (1056 ^ _17875) ^ [_34587, _34589] : [1058 ^ _17875 : [(1061 ^ _17875) ^ [] : [in(1057 ^ [_34587, _34589], _34587)], (1059 ^ _17875) ^ [] : [-(in(1057 ^ [_34587, _34589], _34589))]], -(subset(_34589, _34587))], (1824 ^ _17875) ^ [_46118, _46120, _46122] : [subset(_46122, _46120), -(in(_46118, _46122)), -(subset(_46122, set_difference(_46120, singleton(_46118))))], (2642 ^ _17875) ^ [_57682] : [-(relation_dom(identity_relation(_57682)) = _57682)], (2471 ^ _17875) ^ [_55474, _55476] : [element(_55474, powerset(powerset(_55476))), -(_55474 = empty_set), -(subset_difference(_55476, cast_to_subset(_55476), union_of_subsets(_55476, _55474)) = meet_of_subsets(_55476, complements_of_subsets(_55476, _55474)))], (1937 ^ _17875) ^ [_47645, _47647] : [-(subset(_47647, _47647))], (2682 ^ _17875) ^ [_58257, _58259] : [set_difference(_58259, _58257) = _58259, -(disjoint(_58259, _58257))], (1533 ^ _17875) ^ [] : [true___, -(true___)], (2179 ^ _17875) ^ [_51220] : [relation(_51220), -(subset(_51220, cartesian_product2(relation_dom(_51220), relation_rng(_51220))))], (1521 ^ _17875) ^ [] : [true___, -(true___)], (1615 ^ _17875) ^ [] : [true___, -(true___)], (1910 ^ _17875) ^ [_47241] : [-(empty(1906 ^ [_47241]))], (370 ^ _17875) ^ [_23234, _23236] : [-(set_intersection2(_23236, _23234) = set_intersection2(_23234, _23236))], (2137 ^ _17875) ^ [_50656, _50658, _50660] : [-(subset(_50660, set_intersection2(_50658, _50656))), subset(_50660, _50658), subset(_50660, _50656)], (2296 ^ _17875) ^ [_52908, _52910] : [in(_52910, _52908), -(subset(singleton(_52910), _52908))], (2213 ^ _17875) ^ [_51732] : [-(set_intersection2(_51732, empty_set) = empty_set)], (10 ^ _17875) ^ [_17998, _18000, _18002] : [-(_18002 = _17998), _18002 = _18000, _18000 = _17998], (1652 ^ _17875) ^ [_43841] : [empty(powerset(_43841))], (110 ^ _17875) ^ [_19346, _19348, _19350, _19352] : [-(in(_19350, _19346)), in(_19352, _19348), _19352 = _19350, _19348 = _19346], (2155 ^ _17875) ^ [_50898, _50900, _50902] : [-(subset(_50902, _50898)), subset(_50902, _50900), subset(_50900, _50898)], (420 ^ _17875) ^ [_24054, _24056] : [_24056 = _24054, 423 ^ _17875 : [(426 ^ _17875) ^ [] : [-(subset(_24054, _24056))], (424 ^ _17875) ^ [] : [-(subset(_24056, _24054))]]], (591 ^ _17875) ^ [_27077] : [relation(_27077), 594 ^ _17875 : [(595 ^ _17875) ^ [_27184, _27186] : [_27184 = relation_inverse_image(_27077, _27186), 598 ^ _17875 : [(608 ^ _17875) ^ [_27417] : [-(in(_27417, _27184)), 609 ^ _17875 : [(610 ^ _17875) ^ [_27464] : [in(ordered_pair(_27417, _27464), _27077), in(_27464, _27186)]]], (599 ^ _17875) ^ [_27281] : [in(_27281, _27184), 603 ^ _17875 : [(606 ^ _17875) ^ [] : [-(in(602 ^ [_27077, _27184, _27186, _27281], _27186))], (604 ^ _17875) ^ [] : [-(in(ordered_pair(_27281, 602 ^ [_27077, _27184, _27186, _27281]), _27077))]]]]], (618 ^ _17875) ^ [_27582, _27584] : [-(_27582 = relation_inverse_image(_27077, _27584)), 631 ^ _17875 : [(636 ^ _17875) ^ [] : [in(619 ^ [_27077, _27582, _27584], _27582)], (634 ^ _17875) ^ [] : [-(in(630 ^ [_27077, _27582, _27584], _27584))], (632 ^ _17875) ^ [] : [-(in(ordered_pair(619 ^ [_27077, _27582, _27584], 630 ^ [_27077, _27582, _27584]), _27077))]], 622 ^ _17875 : [(625 ^ _17875) ^ [_27730] : [in(ordered_pair(619 ^ [_27077, _27582, _27584], _27730), _27077), in(_27730, _27584)], (623 ^ _17875) ^ [] : [-(in(619 ^ [_27077, _27582, _27584], _27582))]]]]], (2736 ^ _17875) ^ [_58995, _58997, _58999] : [singleton(_58999) = unordered_pair(_58997, _58995), -(_58999 = _58997)], (2766 ^ _17875) ^ [_59440] : [-(union(powerset(_59440)) = _59440)], (140 ^ _17875) ^ [_19793, _19795, _19797, _19799] : [-(relation_image(_19799, _19795) = relation_image(_19797, _19793)), _19799 = _19797, _19795 = _19793], (2568 ^ _17875) ^ [] : [-(relation_dom(empty_set) = empty_set)], (2427 ^ _17875) ^ [_54784] : [relation(_54784), 2430 ^ _17875 : [(2431 ^ _17875) ^ [_54859] : [relation(_54859), subset(relation_rng(_54784), relation_dom(_54859)), -(relation_dom(relation_composition(_54784, _54859)) = relation_dom(_54784))]]], (2062 ^ _17875) ^ [_49523, _49525] : [subset(_49523, 2042 ^ [_49525]), -(are_equipotent(_49523, 2042 ^ [_49525])), -(in(_49523, 2042 ^ [_49525]))], (2078 ^ _17875) ^ [_49754, _49756, _49758] : [relation(_49754), 2081 ^ _17875 : [(2093 ^ _17875) ^ [] : [-(in(_49758, relation_image(_49754, _49756))), 2094 ^ _17875 : [(2095 ^ _17875) ^ [_50009] : [in(_50009, relation_dom(_49754)), in(ordered_pair(_50009, _49758), _49754), in(_50009, _49756)]]], (2082 ^ _17875) ^ [] : [in(_49758, relation_image(_49754, _49756)), 2086 ^ _17875 : [(2091 ^ _17875) ^ [] : [-(in(2085 ^ [_49754, _49756, _49758], _49756))], (2089 ^ _17875) ^ [] : [-(in(ordered_pair(2085 ^ [_49754, _49756, _49758], _49758), _49754))], (2087 ^ _17875) ^ [] : [-(in(2085 ^ [_49754, _49756, _49758], relation_dom(_49754)))]]]]], (1734 ^ _17875) ^ [_44856, _44858] : [1741 ^ _17875 : [(1744 ^ _17875) ^ [] : [-(relation(relation_composition(_44858, _44856)))], (1742 ^ _17875) ^ [] : [-(empty(relation_composition(_44858, _44856)))]], empty(_44858), relation(_44856)], (1628 ^ _17875) ^ [_43516] : [-(element(1626 ^ [_43516], _43516))], (1441 ^ _17875) ^ [_41326, _41328] : [proper_subset(_41328, _41326), 1444 ^ _17875 : [(1447 ^ _17875) ^ [] : [_41328 = _41326], (1445 ^ _17875) ^ [] : [-(subset(_41328, _41326))]]], (366 ^ _17875) ^ [_23172, _23174] : [-(unordered_pair(_23174, _23172) = unordered_pair(_23172, _23174))], (130 ^ _17875) ^ [_19644, _19646, _19648, _19650] : [-(relation_rng_restriction(_19650, _19646) = relation_rng_restriction(_19648, _19644)), _19650 = _19648, _19646 = _19644], (2119 ^ _17875) ^ [_50374] : [relation(_50374), -(relation_image(_50374, relation_dom(_50374)) = relation_rng(_50374))], (1890 ^ _17875) ^ [_47006] : [-(empty(_47006)), 1894 ^ _17875 : [(1897 ^ _17875) ^ [] : [empty(1893 ^ [_47006])], (1895 ^ _17875) ^ [] : [-(element(1893 ^ [_47006], powerset(_47006)))]]], (1573 ^ _17875) ^ [_42774, _42776] : [element(_42774, powerset(powerset(_42776))), -(element(union_of_subsets(_42776, _42774), powerset(_42776)))], (2674 ^ _17875) ^ [_58135, _58137] : [-(subset(_58137, set_union2(_58137, _58135)))], (2125 ^ _17875) ^ [_50461] : [relation(_50461), 2128 ^ _17875 : [(2129 ^ _17875) ^ [_50529] : [relation(_50529), -(relation_rng(relation_composition(_50461, _50529)) = relation_image(_50529, relation_rng(_50461)))]]], (2149 ^ _17875) ^ [_50821, _50823] : [in(_50823, _50821), -(element(_50823, _50821))], (1642 ^ _17875) ^ [_43703, _43705] : [-(relation(set_intersection2(_43705, _43703))), relation(_43705), relation(_43703)], (1678 ^ _17875) ^ [_44200, _44202] : [-(empty(_44202)), empty(set_union2(_44200, _44202))], (1748 ^ _17875) ^ [_45043, _45045] : [-(set_intersection2(_45045, _45045) = _45045)], (100 ^ _17875) ^ [_19225, _19227] : [-(relation(_19225)), _19227 = _19225, relation(_19227)], (1579 ^ _17875) ^ [_42869] : [-(relation(identity_relation(_42869)))], (1658 ^ _17875) ^ [_43922, _43924] : [-(relation(set_union2(_43924, _43922))), relation(_43924), relation(_43922)], (1772 ^ _17875) ^ [_45413, _45415] : [in(_45415, _45413), -(set_union2(singleton(_45415), _45413) = _45413)], (2072 ^ _17875) ^ [_49653, _49655, _49657] : [relation(_49653), -(relation_dom_restriction(relation_rng_restriction(_49657, _49653), _49655) = relation_rng_restriction(_49657, relation_dom_restriction(_49653, _49655)))], (268 ^ _17875) ^ [_21695, _21697, _21699, _21701] : [-(relation_composition(_21701, _21697) = relation_composition(_21699, _21695)), _21701 = _21699, _21697 = _21695], (1876 ^ _17875) ^ [_46822, _46824] : [1878 ^ _17875 : [(1881 ^ _17875) ^ [] : [in(1877 ^ [_46822, _46824], _46822)], (1879 ^ _17875) ^ [] : [-(in(1877 ^ [_46822, _46824], _46824))]], -(element(_46824, powerset(_46822)))], (1746 ^ _17875) ^ [_45015, _45017] : [-(set_union2(_45017, _45017) = _45017)], (1630 ^ _17875) ^ [_43544, _43546] : [1637 ^ _17875 : [(1640 ^ _17875) ^ [] : [-(relation(relation_composition(_43544, _43546)))], (1638 ^ _17875) ^ [] : [-(empty(relation_composition(_43544, _43546)))]], empty(_43546), relation(_43544)], (1908 ^ _17875) ^ [_47214] : [-(element(1906 ^ [_47214], powerset(_47214)))], (1718 ^ _17875) ^ [_44650] : [empty(_44650), 1721 ^ _17875 : [(1724 ^ _17875) ^ [] : [-(relation(relation_dom(_44650)))], (1722 ^ _17875) ^ [] : [-(empty(relation_dom(_44650)))]]], (1471 ^ _17875) ^ [] : [true___, -(true___)], (2748 ^ _17875) ^ [_59179, _59181] : [in(_59181, _59179), -(subset(_59181, union(_59179)))], (2493 ^ _17875) ^ [_55768] : [-(set_difference(empty_set, _55768) = empty_set)], (770 ^ _17875) ^ [_30016, _30018] : [_30016 = powerset(_30018), 773 ^ _17875 : [(780 ^ _17875) ^ [_30170] : [subset(_30170, _30018), -(in(_30170, _30016))], (774 ^ _17875) ^ [_30095] : [in(_30095, _30016), -(subset(_30095, _30018))]]], (300 ^ _17875) ^ [_22163, _22165] : [_22165 = _22163, -(powerset(_22165) = powerset(_22163))], (1945 ^ _17875) ^ [_47768, _47770, _47772, _47774] : [in(ordered_pair(_47774, _47772), cartesian_product2(_47770, _47768)), 1948 ^ _17875 : [(1951 ^ _17875) ^ [] : [-(in(_47772, _47768))], (1949 ^ _17875) ^ [] : [-(in(_47774, _47770))]]], (1147 ^ _17875) ^ [_36127, _36129] : [_36127 = union(_36129), 1150 ^ _17875 : [(1160 ^ _17875) ^ [_36341] : [-(in(_36341, _36127)), 1161 ^ _17875 : [(1162 ^ _17875) ^ [_36383] : [in(_36341, _36383), in(_36383, _36129)]]], (1151 ^ _17875) ^ [_36217] : [in(_36217, _36127), 1155 ^ _17875 : [(1158 ^ _17875) ^ [] : [-(in(1154 ^ [_36127, _36129, _36217], _36129))], (1156 ^ _17875) ^ [] : [-(in(_36217, 1154 ^ [_36127, _36129, _36217]))]]]]], (2505 ^ _17875) ^ [_55937, _55939] : [-(disjoint(_55939, _55937)), -(in(2508 ^ [_55937, _55939], set_intersection2(_55939, _55937)))], (2147 ^ _17875) ^ [_50795] : [-(set_union2(_50795, empty_set) = _50795)], (2742 ^ _17875) ^ [_59084, _59086] : [relation(_59084), -(relation_dom(relation_dom_restriction(_59084, _59086)) = set_intersection2(relation_dom(_59084), _59086))], (2441 ^ _17875) ^ [_55012, _55014] : [element(_55012, powerset(powerset(_55014))), -(_55012 = empty_set), complements_of_subsets(_55014, _55012) = empty_set], (172 ^ _17875) ^ [_20261, _20263, _20265, _20267] : [-(union_of_subsets(_20267, _20263) = union_of_subsets(_20265, _20261)), _20267 = _20265, _20263 = _20261], (757 ^ _17875) ^ [_29878] : [_29878 = empty_set, 760 ^ _17875 : [(761 ^ _17875) ^ [_29939] : [in(_29939, _29878)]]], (166 ^ _17875) ^ [_20176, _20178] : [_20178 = _20176, -(relation_inverse(_20178) = relation_inverse(_20176))], (857 ^ _17875) ^ [_31404, _31406] : [empty(_31406), 860 ^ _17875 : [(867 ^ _17875) ^ [] : [empty(_31404), -(element(_31404, _31406))], (861 ^ _17875) ^ [] : [element(_31404, _31406), -(empty(_31404))]]], (1465 ^ _17875) ^ [] : [true___, -(true___)], (763 ^ _17875) ^ [_29960] : [-(in(764 ^ [_29960], _29960)), -(_29960 = empty_set)], (306 ^ _17875) ^ [_22248, _22250] : [_22250 = _22248, -(singleton(_22250) = singleton(_22248))], (2001 ^ _17875) ^ [_48535, _48537] : [relation(_48535), -(subset(relation_rng_restriction(_48537, _48535), _48535))], (2804 ^ _17875) ^ [_60123, _60125, _60127] : [singleton(_60127) = unordered_pair(_60125, _60123), -(_60125 = _60123)], (1557 ^ _17875) ^ [] : [true___, -(true___)], (1326 ^ _17875) ^ [_39181, _39183] : [disjoint(_39183, _39181), -(set_intersection2(_39183, _39181) = empty_set)], (786 ^ _17875) ^ [_30251, _30253] : [-(_30251 = powerset(_30253)), 790 ^ _17875 : [(793 ^ _17875) ^ [] : [subset(787 ^ [_30251, _30253], _30253)], (791 ^ _17875) ^ [] : [-(in(787 ^ [_30251, _30253], _30251))]], 794 ^ _17875 : [(797 ^ _17875) ^ [] : [in(787 ^ [_30251, _30253], _30251)], (795 ^ _17875) ^ [] : [-(subset(787 ^ [_30251, _30253], _30253))]]], (1834 ^ _17875) ^ [_46235, _46237] : [subset(_46237, singleton(_46235)), -(_46237 = empty_set), -(_46237 = singleton(_46235))], (1858 ^ _17875) ^ [_46556, _46558, _46560, _46562] : [in(ordered_pair(_46562, _46560), cartesian_product2(_46558, _46556)), 1861 ^ _17875 : [(1864 ^ _17875) ^ [] : [-(in(_46560, _46556))], (1862 ^ _17875) ^ [] : [-(in(_46562, _46558))]]], (2379 ^ _17875) ^ [_54037, _54039] : [-(set_difference(set_union2(_54039, _54037), _54037) = set_difference(_54039, _54037))], (1459 ^ _17875) ^ [] : [true___, -(true___)], (2716 ^ _17875) ^ [_58729, _58731] : [empty(_58731), -(_58731 = _58729), empty(_58729)], (2570 ^ _17875) ^ [] : [-(relation_rng(empty_set) = empty_set)], (2268 ^ _17875) ^ [_52486, _52488] : [-(subset(set_difference(_52488, _52486), _52488))], (1214 ^ _17875) ^ [_37214, _37216, _37218] : [-(_37214 = set_difference(_37218, _37216)), 1226 ^ _17875 : [(1231 ^ _17875) ^ [] : [in(1215 ^ [_37214, _37216, _37218], _37214)], (1229 ^ _17875) ^ [] : [in(1215 ^ [_37214, _37216, _37218], _37216)], (1227 ^ _17875) ^ [] : [-(in(1215 ^ [_37214, _37216, _37218], _37218))]], 1218 ^ _17875 : [(1221 ^ _17875) ^ [] : [in(1215 ^ [_37214, _37216, _37218], _37218), -(in(1215 ^ [_37214, _37216, _37218], _37216))], (1219 ^ _17875) ^ [] : [-(in(1215 ^ [_37214, _37216, _37218], _37214))]]], (1668 ^ _17875) ^ [_44060] : [empty(singleton(_44060))], (2491 ^ _17875) ^ [_55734, _55736] : [-(set_difference(_55736, set_difference(_55736, _55734)) = set_intersection2(_55736, _55734))], (2107 ^ _17875) ^ [_50192, _50194] : [relation(_50192), -(subset(relation_image(_50192, _50194), relation_rng(_50192)))], (2044 ^ _17875) ^ [_49245] : [-(in(_49245, 2042 ^ [_49245]))], (1545 ^ _17875) ^ [_42452] : [relation(_42452), -(relation(relation_inverse(_42452)))], (2546 ^ _17875) ^ [_56488] : [relation(_56488), -(in(ordered_pair(2551 ^ [_56488], 2552 ^ [_56488]), _56488)), -(_56488 = empty_set)], (2622 ^ _17875) ^ [_57455, _57457] : [-(in(_57455, _57457)), -(set_difference(_57457, singleton(_57455)) = _57457)], (2056 ^ _17875) ^ [_49426, _49428] : [in(_49426, 2042 ^ [_49428]), -(in(powerset(_49426), 2042 ^ [_49428]))], (2572 ^ _17875) ^ [_56769, _56771] : [subset(_56771, _56769), proper_subset(_56769, _56771)], (2558 ^ _17875) ^ [_56602, _56604, _56606] : [in(_56606, _56604), element(_56604, powerset(_56602)), empty(_56602)], (2225 ^ _17875) ^ [_51846, _51848] : [-(_51848 = _51846), 2229 ^ _17875 : [(2232 ^ _17875) ^ [] : [in(2226 ^ [_51846, _51848], _51846)], (2230 ^ _17875) ^ [] : [-(in(2226 ^ [_51846, _51848], _51848))]], 2233 ^ _17875 : [(2236 ^ _17875) ^ [] : [in(2226 ^ [_51846, _51848], _51848)], (2234 ^ _17875) ^ [] : [-(in(2226 ^ [_51846, _51848], _51846))]]], (1581 ^ _17875) ^ [_42893, _42895] : [element(_42893, powerset(powerset(_42895))), -(element(meet_of_subsets(_42895, _42893), powerset(_42895)))], (1796 ^ _17875) ^ [_45706, _45708] : [in(_45708, _45706), -(subset(singleton(_45708), _45706))], (652 ^ _17875) ^ [_28181] : [654 ^ _17875 : [(657 ^ _17875) ^ [_28294, _28296] : [653 ^ [_28181] = ordered_pair(_28296, _28294)], (655 ^ _17875) ^ [] : [-(in(653 ^ [_28181], _28181))]], -(relation(_28181))], (348 ^ _17875) ^ [_22945, _22947] : [in(_22947, _22945), in(_22945, _22947)], (232 ^ _17875) ^ [_21163, _21165, _21167, _21169] : [-(set_difference(_21169, _21165) = set_difference(_21167, _21163)), _21169 = _21167, _21165 = _21163], (1802 ^ _17875) ^ [_45804, _45806] : [set_difference(_45806, _45804) = empty_set, -(subset(_45806, _45804))], (2710 ^ _17875) ^ [_58648, _58650] : [relation(_58648), -(subset(relation_dom_restriction(_58648, _58650), _58648))], (2242 ^ _17875) ^ [_52105, _52107, _52109] : [relation(_52105), in(ordered_pair(_52109, _52107), _52105), 2249 ^ _17875 : [(2252 ^ _17875) ^ [] : [-(in(_52107, relation_field(_52105)))], (2250 ^ _17875) ^ [] : [-(in(_52109, relation_field(_52105)))]]], (2363 ^ _17875) ^ [_53815, _53817] : [disjoint(_53817, _53815), 2364 ^ _17875 : [(2365 ^ _17875) ^ [_53855] : [in(_53855, _53817), in(_53855, _53815)]]], (2646 ^ _17875) ^ [_57735, _57737, _57739, _57741] : [relation(_57735), 2649 ^ _17875 : [(2658 ^ _17875) ^ [] : [-(in(ordered_pair(_57741, _57739), relation_composition(identity_relation(_57737), _57735))), in(_57741, _57737), in(ordered_pair(_57741, _57739), _57735)], (2650 ^ _17875) ^ [] : [in(ordered_pair(_57741, _57739), relation_composition(identity_relation(_57737), _57735)), 2653 ^ _17875 : [(2656 ^ _17875) ^ [] : [-(in(ordered_pair(_57741, _57739), _57735))], (2654 ^ _17875) ^ [] : [-(in(_57741, _57737))]]]]], (1539 ^ _17875) ^ [] : [true___, -(true___)], (2007 ^ _17875) ^ [_48616, _48618] : [relation(_48616), -(subset(relation_rng(relation_rng_restriction(_48618, _48616)), relation_rng(_48616)))], (1501 ^ _17875) ^ [_41980] : [-(element(cast_to_subset(_41980), powerset(_41980)))], (1272 ^ _17875) ^ [_38235, _38237] : [element(_38235, powerset(_38237)), -(subset_complement(_38237, _38235) = set_difference(_38237, _38235))], (2284 ^ _17875) ^ [_52731, _52733] : [subset(_52733, _52731), -(set_difference(_52733, _52731) = empty_set)], (1762 ^ _17875) ^ [_45245, _45247] : [element(_45245, powerset(powerset(_45247))), -(complements_of_subsets(_45247, complements_of_subsets(_45247, _45245)) = _45245)], (1145 ^ _17875) ^ [_36087] : [-(cast_to_subset(_36087) = _36087)], (2676 ^ _17875) ^ [_58178, _58180] : [disjoint(_58180, _58178), -(set_difference(_58180, _58178) = _58180)], (1698 ^ _17875) ^ [_44396] : [empty(relation_dom(_44396)), -(empty(_44396)), relation(_44396)], (1338 ^ _17875) ^ [_39345] : [relation(_39345), 1341 ^ _17875 : [(1342 ^ _17875) ^ [_39458] : [relation(_39458), 1345 ^ _17875 : [(1346 ^ _17875) ^ [_39563] : [relation(_39563), 1349 ^ _17875 : [(1350 ^ _17875) ^ [] : [_39563 = relation_composition(_39345, _39458), 1353 ^ _17875 : [(1363 ^ _17875) ^ [_39887, _39889] : [-(in(ordered_pair(_39889, _39887), _39563)), 1364 ^ _17875 : [(1365 ^ _17875) ^ [_39942] : [in(ordered_pair(_39889, _39942), _39345), in(ordered_pair(_39942, _39887), _39458)]]], (1354 ^ _17875) ^ [_39733, _39735] : [in(ordered_pair(_39735, _39733), _39563), 1358 ^ _17875 : [(1361 ^ _17875) ^ [] : [-(in(ordered_pair(1357 ^ [_39345, _39458, _39563, _39733, _39735], _39733), _39458))], (1359 ^ _17875) ^ [] : [-(in(ordered_pair(_39735, 1357 ^ [_39345, _39458, _39563, _39733, _39735]), _39345))]]]]], (1373 ^ _17875) ^ [] : [-(_39563 = relation_composition(_39345, _39458)), 1387 ^ _17875 : [(1392 ^ _17875) ^ [] : [in(ordered_pair(1374 ^ [_39345, _39458, _39563], 1375 ^ [_39345, _39458, _39563]), _39563)], (1390 ^ _17875) ^ [] : [-(in(ordered_pair(1386 ^ [_39345, _39458, _39563], 1375 ^ [_39345, _39458, _39563]), _39458))], (1388 ^ _17875) ^ [] : [-(in(ordered_pair(1374 ^ [_39345, _39458, _39563], 1386 ^ [_39345, _39458, _39563]), _39345))]], 1378 ^ _17875 : [(1381 ^ _17875) ^ [_40219] : [in(ordered_pair(1374 ^ [_39345, _39458, _39563], _40219), _39345), in(ordered_pair(_40219, 1375 ^ [_39345, _39458, _39563]), _39458)], (1379 ^ _17875) ^ [] : [-(in(ordered_pair(1374 ^ [_39345, _39458, _39563], 1375 ^ [_39345, _39458, _39563]), _39563))]]]]]]]]], (2512 ^ _17875) ^ [_55979, _55981] : [2513 ^ _17875 : [(2514 ^ _17875) ^ [_56021] : [in(_56021, set_intersection2(_55981, _55979))]], disjoint(_55981, _55979)], (2536 ^ _17875) ^ [_56344, _56346, _56348] : [element(_56344, powerset(_56348)), in(_56346, subset_complement(_56348, _56344)), in(_56346, _56344)], (212 ^ _17875) ^ [_20865, _20867, _20869, _20871] : [-(meet_of_subsets(_20871, _20867) = meet_of_subsets(_20869, _20865)), _20871 = _20869, _20867 = _20865], (2278 ^ _17875) ^ [_52652, _52654] : [set_difference(_52654, _52652) = empty_set, -(subset(_52654, _52652))], (1888 ^ _17875) ^ [] : [-(relation(1884 ^ []))], (916 ^ _17875) ^ [_32266, _32268, _32270] : [_32266 = set_union2(_32270, _32268), 919 ^ _17875 : [(920 ^ _17875) ^ [_32355] : [in(_32355, _32266), -(in(_32355, _32270)), -(in(_32355, _32268))], (930 ^ _17875) ^ [_32445] : [931 ^ _17875 : [(934 ^ _17875) ^ [] : [in(_32445, _32268)], (932 ^ _17875) ^ [] : [in(_32445, _32270)]], -(in(_32445, _32266))]]], (294 ^ _17875) ^ [_22078, _22080] : [_22080 = _22078, -(union(_22080) = union(_22078))], (1814 ^ _17875) ^ [_45968, _45970] : [element(_45968, powerset(_45970)), 1817 ^ _17875 : [(1818 ^ _17875) ^ [_46035] : [in(_46035, _45968), -(in(_46035, _45970))]]], (2354 ^ _17875) ^ [_53732, _53734] : [-(disjoint(_53734, _53732)), 2358 ^ _17875 : [(2361 ^ _17875) ^ [] : [-(in(2357 ^ [_53732, _53734], _53732))], (2359 ^ _17875) ^ [] : [-(in(2357 ^ [_53732, _53734], _53734))]]], (1597 ^ _17875) ^ [_43141, _43143] : [relation(_43143), -(relation(relation_dom_restriction(_43143, _43141)))], (62 ^ _17875) ^ [_18714, _18716] : [-(empty(_18714)), _18716 = _18714, empty(_18716)], (2644 ^ _17875) ^ [_57706] : [-(relation_rng(identity_relation(_57706)) = _57706)], (1808 ^ _17875) ^ [_45883, _45885] : [subset(_45885, _45883), -(set_difference(_45885, _45883) = empty_set)], (360 ^ _17875) ^ [_23101] : [empty(_23101), -(relation(_23101))], (1609 ^ _17875) ^ [_43319, _43321] : [relation(_43319), -(relation(relation_rng_restriction(_43321, _43319)))], (1852 ^ _17875) ^ [_46454, _46456] : [in(_46456, _46454), -(subset(_46456, union(_46454)))], (2688 ^ _17875) ^ [_58342, _58344, _58346] : [relation(_58342), 2691 ^ _17875 : [(2700 ^ _17875) ^ [] : [-(in(_58346, relation_dom(relation_dom_restriction(_58342, _58344)))), in(_58346, _58344), in(_58346, relation_dom(_58342))], (2692 ^ _17875) ^ [] : [in(_58346, relation_dom(relation_dom_restriction(_58342, _58344))), 2695 ^ _17875 : [(2698 ^ _17875) ^ [] : [-(in(_58346, relation_dom(_58342)))], (2696 ^ _17875) ^ [] : [-(in(_58346, _58344))]]]]], (312 ^ _17875) ^ [_22333, _22335, _22337, _22339] : [-(unordered_pair(_22339, _22335) = unordered_pair(_22337, _22333)), _22339 = _22337, _22335 = _22333], (1708 ^ _17875) ^ [_44523] : [empty(relation_rng(_44523)), -(empty(_44523)), relation(_44523)], (1495 ^ _17875) ^ [] : [true___, -(true___)], (1170 ^ _17875) ^ [_36493, _36495] : [-(_36493 = union(_36495)), 1183 ^ _17875 : [(1188 ^ _17875) ^ [] : [in(1171 ^ [_36493, _36495], _36493)], (1186 ^ _17875) ^ [] : [-(in(1182 ^ [_36493, _36495], _36495))], (1184 ^ _17875) ^ [] : [-(in(1171 ^ [_36493, _36495], 1182 ^ [_36493, _36495]))]], 1174 ^ _17875 : [(1177 ^ _17875) ^ [_36626] : [in(1171 ^ [_36493, _36495], _36626), in(_36626, _36495)], (1175 ^ _17875) ^ [] : [-(in(1171 ^ [_36493, _36495], _36493))]]], (1046 ^ _17875) ^ [_34445, _34447] : [subset(_34447, _34445), 1049 ^ _17875 : [(1050 ^ _17875) ^ [_34508] : [in(_34508, _34447), -(in(_34508, _34445))]]], (1686 ^ _17875) ^ [] : [-(relation(empty_set))], (2302 ^ _17875) ^ [_53009, _53011, _53013] : [subset(unordered_pair(_53013, _53011), _53009), 2305 ^ _17875 : [(2308 ^ _17875) ^ [] : [-(in(_53011, _53009))], (2306 ^ _17875) ^ [] : [-(in(_53013, _53009))]]], (2578 ^ _17875) ^ [_56845, _56847, _56849] : [-(disjoint(_56849, _56845)), subset(_56849, _56847), disjoint(_56847, _56845)], (1087 ^ _17875) ^ [_35078, _35080, _35082] : [-(_35078 = set_intersection2(_35082, _35080)), 1099 ^ _17875 : [(1104 ^ _17875) ^ [] : [in(1088 ^ [_35078, _35080, _35082], _35078)], (1102 ^ _17875) ^ [] : [-(in(1088 ^ [_35078, _35080, _35082], _35080))], (1100 ^ _17875) ^ [] : [-(in(1088 ^ [_35078, _35080, _35082], _35082))]], 1091 ^ _17875 : [(1094 ^ _17875) ^ [] : [in(1088 ^ [_35078, _35080, _35082], _35082), in(1088 ^ [_35078, _35080, _35082], _35080)], (1092 ^ _17875) ^ [] : [-(in(1088 ^ [_35078, _35080, _35082], _35078))]]], (1905 ^ _17875) ^ [] : [-(relation(1901 ^ []))], (1563 ^ _17875) ^ [_42645, _42647] : [-(relation(relation_composition(_42647, _42645))), relation(_42647), relation(_42645)], (86 ^ _17875) ^ [_19032, _19034, _19036, _19038] : [-(are_equipotent(_19036, _19032)), are_equipotent(_19038, _19034), _19038 = _19036, _19034 = _19032], (2135 ^ _17875) ^ [_50628, _50630] : [-(subset(set_intersection2(_50630, _50628), _50630))], (2342 ^ _17875) ^ [_53566, _53568] : [element(_53568, powerset(_53566)), -(subset(_53568, _53566))], (262 ^ _17875) ^ [_21610, _21612] : [_21612 = _21610, -(relation_dom(_21612) = relation_dom(_21610))], (1551 ^ _17875) ^ [] : [true___, -(true___)], (742 ^ _17875) ^ [_29624, _29626] : [-(_29624 = singleton(_29626)), 746 ^ _17875 : [(749 ^ _17875) ^ [] : [743 ^ [_29624, _29626] = _29626], (747 ^ _17875) ^ [] : [-(in(743 ^ [_29624, _29626], _29624))]], 750 ^ _17875 : [(753 ^ _17875) ^ [] : [in(743 ^ [_29624, _29626], _29624)], (751 ^ _17875) ^ [] : [-(743 ^ [_29624, _29626] = _29626)]]], (938 ^ _17875) ^ [_32566, _32568, _32570] : [-(_32566 = set_union2(_32570, _32568)), 942 ^ _17875 : [(947 ^ _17875) ^ [] : [in(939 ^ [_32566, _32568, _32570], _32568)], (945 ^ _17875) ^ [] : [in(939 ^ [_32566, _32568, _32570], _32570)], (943 ^ _17875) ^ [] : [-(in(939 ^ [_32566, _32568, _32570], _32566))]], 948 ^ _17875 : [(949 ^ _17875) ^ [] : [-(in(939 ^ [_32566, _32568, _32570], _32570)), -(in(939 ^ [_32566, _32568, _32570], _32568))], (955 ^ _17875) ^ [] : [in(939 ^ [_32566, _32568, _32570], _32566)]]], (2322 ^ _17875) ^ [_53306, _53308] : [subset(_53308, singleton(_53306)), -(_53308 = empty_set), -(_53308 = singleton(_53306))], (2754 ^ _17875) ^ [_59260, _59262] : [relation(_59260), -(relation_dom_restriction(_59260, _59262) = relation_composition(identity_relation(_59262), _59260))], (2332 ^ _17875) ^ [_53400, _53402] : [2333 ^ _17875 : [(2336 ^ _17875) ^ [] : [_53402 = singleton(_53400)], (2334 ^ _17875) ^ [] : [_53402 = empty_set]], -(subset(_53402, singleton(_53400)))], (4 ^ _17875) ^ [_17925, _17927] : [_17927 = _17925, -(_17925 = _17927)], (1995 ^ _17875) ^ [_48450, _48452] : [relation(_48450), -(subset(relation_rng(relation_rng_restriction(_48452, _48450)), _48452))], (2628 ^ _17875) ^ [_57498] : [-(unordered_pair(_57498, _57498) = singleton(_57498))], (2616 ^ _17875) ^ [_57373, _57375] : [set_difference(_57375, singleton(_57373)) = _57375, in(_57373, _57375)], (2046 ^ _17875) ^ [_49273, _49275, _49277] : [-(in(_49273, 2042 ^ [_49277])), in(_49275, 2042 ^ [_49277]), subset(_49273, _49275)], (490 ^ _17875) ^ [_25233, _25235] : [relation(_25233), 493 ^ _17875 : [(494 ^ _17875) ^ [_25330] : [relation(_25330), 497 ^ _17875 : [(498 ^ _17875) ^ [] : [_25330 = relation_rng_restriction(_25235, _25233), 501 ^ _17875 : [(510 ^ _17875) ^ [_25609, _25611] : [-(in(ordered_pair(_25611, _25609), _25330)), in(_25609, _25235), in(ordered_pair(_25611, _25609), _25233)], (502 ^ _17875) ^ [_25492, _25494] : [in(ordered_pair(_25494, _25492), _25330), 505 ^ _17875 : [(508 ^ _17875) ^ [] : [-(in(ordered_pair(_25494, _25492), _25233))], (506 ^ _17875) ^ [] : [-(in(_25492, _25235))]]]]], (520 ^ _17875) ^ [] : [-(_25330 = relation_rng_restriction(_25235, _25233)), 533 ^ _17875 : [(538 ^ _17875) ^ [] : [in(ordered_pair(521 ^ [_25233, _25235, _25330], 522 ^ [_25233, _25235, _25330]), _25330)], (536 ^ _17875) ^ [] : [-(in(ordered_pair(521 ^ [_25233, _25235, _25330], 522 ^ [_25233, _25235, _25330]), _25233))], (534 ^ _17875) ^ [] : [-(in(522 ^ [_25233, _25235, _25330], _25235))]], 525 ^ _17875 : [(528 ^ _17875) ^ [] : [in(522 ^ [_25233, _25235, _25330], _25235), in(ordered_pair(521 ^ [_25233, _25235, _25330], 522 ^ [_25233, _25235, _25330]), _25233)], (526 ^ _17875) ^ [] : [-(in(ordered_pair(521 ^ [_25233, _25235, _25330], 522 ^ [_25233, _25235, _25330]), _25330))]]]]]]], (2401 ^ _17875) ^ [_54379] : [relation(_54379), 2404 ^ _17875 : [(2405 ^ _17875) ^ [_54444] : [relation(_54444), -(subset(relation_dom(relation_composition(_54379, _54444)), relation_dom(_54379)))]]], (2215 ^ _17875) ^ [_51758, _51760] : [element(_51760, _51758), -(empty(_51758)), -(in(_51760, _51758))], (2037 ^ _17875) ^ [_49078, _49080] : [subset(_49080, _49078), -(set_union2(_49080, _49078) = _49078)], (1065 ^ _17875) ^ [_34747, _34749, _34751] : [_34747 = set_intersection2(_34751, _34749), 1068 ^ _17875 : [(1077 ^ _17875) ^ [_34939] : [-(in(_34939, _34747)), in(_34939, _34751), in(_34939, _34749)], (1069 ^ _17875) ^ [_34836] : [in(_34836, _34747), 1072 ^ _17875 : [(1075 ^ _17875) ^ [] : [-(in(_34836, _34749))], (1073 ^ _17875) ^ [] : [-(in(_34836, _34751))]]]]], (1886 ^ _17875) ^ [] : [-(empty(1884 ^ []))], (2348 ^ _17875) ^ [_53643, _53645] : [subset(_53645, _53643), -(element(_53645, powerset(_53643)))], (1286 ^ _17875) ^ [_38455] : [relation(_38455), 1289 ^ _17875 : [(1290 ^ _17875) ^ [_38543] : [relation(_38543), 1293 ^ _17875 : [(1294 ^ _17875) ^ [] : [_38543 = relation_inverse(_38455), 1297 ^ _17875 : [(1304 ^ _17875) ^ [_38782, _38784] : [in(ordered_pair(_38782, _38784), _38455), -(in(ordered_pair(_38784, _38782), _38543))], (1298 ^ _17875) ^ [_38693, _38695] : [in(ordered_pair(_38695, _38693), _38543), -(in(ordered_pair(_38693, _38695), _38455))]]], (1310 ^ _17875) ^ [] : [-(_38543 = relation_inverse(_38455)), 1315 ^ _17875 : [(1318 ^ _17875) ^ [] : [in(ordered_pair(1312 ^ [_38455, _38543], 1311 ^ [_38455, _38543]), _38455)], (1316 ^ _17875) ^ [] : [-(in(ordered_pair(1311 ^ [_38455, _38543], 1312 ^ [_38455, _38543]), _38543))]], 1319 ^ _17875 : [(1322 ^ _17875) ^ [] : [in(ordered_pair(1311 ^ [_38455, _38543], 1312 ^ [_38455, _38543]), _38543)], (1320 ^ _17875) ^ [] : [-(in(ordered_pair(1312 ^ [_38455, _38543], 1311 ^ [_38455, _38543]), _38455))]]]]]]], (368 ^ _17875) ^ [_23203, _23205] : [-(set_union2(_23205, _23203) = set_union2(_23203, _23205))], (332 ^ _17875) ^ [_22631, _22633] : [_22633 = _22631, -(relation_rng(_22633) = relation_rng(_22631))], (1913 ^ _17875) ^ [] : [empty(1911 ^ [])], (2310 ^ _17875) ^ [_53116, _53118, _53120] : [-(subset(unordered_pair(_53120, _53118), _53116)), in(_53120, _53116), in(_53118, _53116)], (1527 ^ _17875) ^ [_42243, _42245] : [element(_42243, powerset(_42245)), -(element(subset_complement(_42245, _42243), powerset(_42245)))], (2495 ^ _17875) ^ [_55794, _55796, _55798] : [-(element(_55798, _55794)), in(_55798, _55796), element(_55796, powerset(_55794))], (2027 ^ _17875) ^ [_48929, _48931, _48933, _48935] : [-(subset(cartesian_product2(_48935, _48931), cartesian_product2(_48933, _48929))), subset(_48935, _48933), subset(_48931, _48929)], (1939 ^ _17875) ^ [_47670, _47672] : [disjoint(_47672, _47670), -(disjoint(_47670, _47672))], (661 ^ _17875) ^ [_28366, _28368] : [-(_28368 = empty_set), 664 ^ _17875 : [(665 ^ _17875) ^ [] : [_28366 = set_meet(_28368), 668 ^ _17875 : [(669 ^ _17875) ^ [_28513] : [in(_28513, _28366), 672 ^ _17875 : [(673 ^ _17875) ^ [_28578] : [in(_28578, _28368), -(in(_28513, _28578))]]], (679 ^ _17875) ^ [_28659] : [681 ^ _17875 : [(684 ^ _17875) ^ [] : [in(_28659, 680 ^ [_28366, _28368, _28659])], (682 ^ _17875) ^ [] : [-(in(680 ^ [_28366, _28368, _28659], _28368))]], -(in(_28659, _28366))]]], (688 ^ _17875) ^ [] : [-(_28366 = set_meet(_28368)), 692 ^ _17875 : [(698 ^ _17875) ^ [] : [in(689 ^ [_28366, _28368], 694 ^ [_28366, _28368])], (696 ^ _17875) ^ [] : [-(in(694 ^ [_28366, _28368], _28368))], (693 ^ _17875) ^ [] : [-(in(689 ^ [_28366, _28368], _28366))]], 699 ^ _17875 : [(700 ^ _17875) ^ [_29003] : [in(_29003, _28368), -(in(689 ^ [_28366, _28368], _29003))], (706 ^ _17875) ^ [] : [in(689 ^ [_28366, _28368], _28366)]]]]], (959 ^ _17875) ^ [_32906, _32908, _32910] : [_32906 = cartesian_product2(_32910, _32908), 962 ^ _17875 : [(975 ^ _17875) ^ [_33201] : [-(in(_33201, _32906)), 976 ^ _17875 : [(977 ^ _17875) ^ [_33259, _33261] : [in(_33261, _32910), in(_33259, _32908), _33201 = ordered_pair(_33261, _33259)]]], (963 ^ _17875) ^ [_33014] : [in(_33014, _32906), 968 ^ _17875 : [(973 ^ _17875) ^ [] : [-(_33014 = ordered_pair(966 ^ [_32906, _32908, _32910, _33014], 967 ^ [_32906, _32908, _32910, _33014]))], (971 ^ _17875) ^ [] : [-(in(967 ^ [_32906, _32908, _32910, _33014], _32908))], (969 ^ _17875) ^ [] : [-(in(966 ^ [_32906, _32908, _32910, _33014], _32910))]]]]], (338 ^ _17875) ^ [_22712, _22714, _22716, _22718] : [-(ordered_pair(_22718, _22714) = ordered_pair(_22716, _22712)), _22718 = _22716, _22714 = _22712], (1844 ^ _17875) ^ [_46329, _46331] : [1845 ^ _17875 : [(1848 ^ _17875) ^ [] : [_46331 = singleton(_46329)], (1846 ^ _17875) ^ [] : [_46331 = empty_set]], -(subset(_46331, singleton(_46329)))], (1515 ^ _17875) ^ [] : [true___, -(true___)], (2373 ^ _17875) ^ [_53962] : [subset(_53962, empty_set), -(_53962 = empty_set)], (640 ^ _17875) ^ [_27996] : [relation(_27996), 643 ^ _17875 : [(644 ^ _17875) ^ [_28072] : [in(_28072, _27996), -(_28072 = ordered_pair(647 ^ [_27996, _28072], 648 ^ [_27996, _28072]))]]], (710 ^ _17875) ^ [_29159, _29161] : [_29161 = empty_set, 713 ^ _17875 : [(720 ^ _17875) ^ [] : [_29159 = empty_set, -(_29159 = set_meet(_29161))], (714 ^ _17875) ^ [] : [_29159 = set_meet(_29161), -(_29159 = empty_set)]]]], input).
% 64.42/62.53 ncf('1',plain,[2832 : -(in(ordered_pair(2809 ^ [], 2828 ^ []), 2811 ^ [])), 2819 : in(602 ^ [2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []), 2810 ^ [], 2809 ^ []], relation_rng(2811 ^ [])), 2819 : in(ordered_pair(2809 ^ [], 602 ^ [2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []), 2810 ^ [], 2809 ^ []]), 2811 ^ []), 2819 : in(602 ^ [2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []), 2810 ^ [], 2809 ^ []], 2810 ^ [])],start(2815 ^ 0,bind([[_61566], [602 ^ [2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []), 2810 ^ [], 2809 ^ []]]]))).
% 64.42/62.53 ncf('1.1',plain,[in(ordered_pair(2809 ^ [], 2828 ^ []), 2811 ^ []), -(in(ordered_pair(ordered_pair(2809 ^ [], 2828 ^ []), 2809 ^ []), cartesian_product2(2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ [])))), in(2809 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []))],extension(1953 ^ 3,bind([[_47883, _47885, _47887, _47889], [relation_inverse_image(2811 ^ [], 2810 ^ []), 2811 ^ [], 2809 ^ [], ordered_pair(2809 ^ [], 2828 ^ [])]]))).
% 64.42/62.53 ncf('1.1.1',plain,[in(ordered_pair(ordered_pair(2809 ^ [], 2828 ^ []), 2809 ^ []), cartesian_product2(2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []))), -(in(ordered_pair(ordered_pair(ordered_pair(2809 ^ [], 2828 ^ []), 2809 ^ []), 2809 ^ []), cartesian_product2(cartesian_product2(2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ [])), relation_inverse_image(2811 ^ [], 2810 ^ [])))), in(2809 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []))],extension(1953 ^ 4,bind([[_47883, _47885, _47887, _47889], [relation_inverse_image(2811 ^ [], 2810 ^ []), cartesian_product2(2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ [])), 2809 ^ [], ordered_pair(ordered_pair(2809 ^ [], 2828 ^ []), 2809 ^ [])]]))).
% 64.42/62.53 ncf('1.1.1.1',plain,[in(ordered_pair(ordered_pair(ordered_pair(2809 ^ [], 2828 ^ []), 2809 ^ []), 2809 ^ []), cartesian_product2(cartesian_product2(2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ [])), relation_inverse_image(2811 ^ [], 2810 ^ []))), 1951 : -(in(2809 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ [])))],extension(1945 ^ 5,bind([[_47768, _47770, _47772, _47774], [relation_inverse_image(2811 ^ [], 2810 ^ []), cartesian_product2(2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ [])), 2809 ^ [], ordered_pair(ordered_pair(2809 ^ [], 2828 ^ []), 2809 ^ [])]]))).
% 64.42/62.54 ncf('1.1.1.1.1',plain,[in(2809 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []))],extension(2836 ^ 8)).
% 64.42/62.54 ncf('1.1.1.2',plain,[-(in(2809 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []))), in(ordered_pair(ordered_pair(2809 ^ [], 2828 ^ []), 2809 ^ []), cartesian_product2(2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ [])))],extension(1945 ^ 5,bind([[_47768, _47770, _47772, _47774], [relation_inverse_image(2811 ^ [], 2810 ^ []), 2811 ^ [], 2809 ^ [], ordered_pair(2809 ^ [], 2828 ^ [])]]))).
% 64.42/62.54 ncf('1.1.1.2.1',plain,[-(in(ordered_pair(ordered_pair(2809 ^ [], 2828 ^ []), 2809 ^ []), cartesian_product2(2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []))))],reduction('1.1')).
% 64.42/62.54 ncf('1.1.2',plain,[-(in(2809 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []))), 610 : in(ordered_pair(2809 ^ [], 2828 ^ []), 2811 ^ []), 610 : in(2828 ^ [], 2810 ^ []), 608 : relation_inverse_image(2811 ^ [], 2810 ^ []) = relation_inverse_image(2811 ^ [], 2810 ^ []), 595 : relation(2811 ^ [])],extension(591 ^ 4,bind([[_27077, _27184, _27186, _27417, _27464], [2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []), 2810 ^ [], 2809 ^ [], 2828 ^ []]]))).
% 64.42/62.54 ncf('1.1.2.1',plain,[-(in(ordered_pair(2809 ^ [], 2828 ^ []), 2811 ^ []))],reduction('1')).
% 64.42/62.54 ncf('1.1.2.2',plain,[-(in(2828 ^ [], 2810 ^ []))],extension(2834 ^ 11)).
% 64.42/62.54 ncf('1.1.2.3',plain,[-(relation_inverse_image(2811 ^ [], 2810 ^ []) = relation_inverse_image(2811 ^ [], 2810 ^ []))],extension(2 ^ 7,bind([[_17902], [relation_inverse_image(2811 ^ [], 2810 ^ [])]]))).
% 64.42/62.54 ncf('1.1.2.4',plain,[-(relation(2811 ^ []))],extension(2813 ^ 5)).
% 64.42/62.54 ncf('1.2',plain,[-(in(602 ^ [2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []), 2810 ^ [], 2809 ^ []], relation_rng(2811 ^ []))), relation(2811 ^ []), in(ordered_pair(2809 ^ [], 602 ^ [2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []), 2810 ^ [], 2809 ^ []]), 2811 ^ [])],extension(2167 ^ 3,bind([[_51049, _51051, _51053], [2811 ^ [], 602 ^ [2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []), 2810 ^ [], 2809 ^ []], 2809 ^ []]]))).
% 64.42/62.54 ncf('1.2.1',plain,[-(relation(2811 ^ []))],extension(2813 ^ 4)).
% 64.42/62.54 ncf('1.2.2',plain,[-(in(ordered_pair(2809 ^ [], 602 ^ [2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []), 2810 ^ [], 2809 ^ []]), 2811 ^ [])), 599 : in(2809 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ [])), 599 : relation_inverse_image(2811 ^ [], 2810 ^ []) = relation_inverse_image(2811 ^ [], 2810 ^ []), 595 : relation(2811 ^ [])],extension(591 ^ 4,bind([[_27077, _27184, _27186, _27281], [2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []), 2810 ^ [], 2809 ^ []]]))).
% 64.42/62.54 ncf('1.2.2.1',plain,[-(in(2809 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ [])))],extension(2817 ^ 9)).
% 64.42/62.54 ncf('1.2.2.2',plain,[-(relation_inverse_image(2811 ^ [], 2810 ^ []) = relation_inverse_image(2811 ^ [], 2810 ^ []))],extension(2 ^ 7,bind([[_17902], [relation_inverse_image(2811 ^ [], 2810 ^ [])]]))).
% 64.42/62.54 ncf('1.2.2.3',plain,[-(relation(2811 ^ []))],lemmata('[1].x')).
% 64.42/62.54 ncf('1.3',plain,[-(in(ordered_pair(2809 ^ [], 602 ^ [2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []), 2810 ^ [], 2809 ^ []]), 2811 ^ [])), 599 : in(2809 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ [])), 599 : relation_inverse_image(2811 ^ [], 2810 ^ []) = relation_inverse_image(2811 ^ [], 2810 ^ []), 595 : relation(2811 ^ [])],extension(591 ^ 3,bind([[_27077, _27184, _27186, _27281], [2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []), 2810 ^ [], 2809 ^ []]]))).
% 64.42/62.54 ncf('1.3.1',plain,[-(in(2809 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ [])))],extension(2817 ^ 8)).
% 64.42/62.54 ncf('1.3.2',plain,[-(relation_inverse_image(2811 ^ [], 2810 ^ []) = relation_inverse_image(2811 ^ [], 2810 ^ [])), unordered_pair(relation_inverse_image(2811 ^ [], 2810 ^ []), relation_inverse_image(2811 ^ [], 2810 ^ [])) = unordered_pair(relation_inverse_image(2811 ^ [], 2810 ^ []), relation_inverse_image(2811 ^ [], 2810 ^ [])), -(relation_inverse_image(2811 ^ [], 2810 ^ []) = relation_inverse_image(2811 ^ [], 2810 ^ []))],extension(1963 ^ 6,bind([[_48034, _48036, _48038, _48040], [relation_inverse_image(2811 ^ [], 2810 ^ []), relation_inverse_image(2811 ^ [], 2810 ^ []), relation_inverse_image(2811 ^ [], 2810 ^ []), relation_inverse_image(2811 ^ [], 2810 ^ [])]]))).
% 64.42/62.54 ncf('1.3.2.1',plain,[-(unordered_pair(relation_inverse_image(2811 ^ [], 2810 ^ []), relation_inverse_image(2811 ^ [], 2810 ^ [])) = unordered_pair(relation_inverse_image(2811 ^ [], 2810 ^ []), relation_inverse_image(2811 ^ [], 2810 ^ [])))],extension(2 ^ 7,bind([[_17902], [unordered_pair(relation_inverse_image(2811 ^ [], 2810 ^ []), relation_inverse_image(2811 ^ [], 2810 ^ []))]]))).
% 64.42/62.54 ncf('1.3.2.2',plain,[relation_inverse_image(2811 ^ [], 2810 ^ []) = relation_inverse_image(2811 ^ [], 2810 ^ [])],reduction('1.3')).
% 64.42/62.54 ncf('1.3.3',plain,[-(relation(2811 ^ []))],extension(2813 ^ 4)).
% 64.42/62.54 ncf('1.4',plain,[-(in(602 ^ [2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []), 2810 ^ [], 2809 ^ []], 2810 ^ [])), 599 : in(2809 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ [])), 599 : relation_inverse_image(2811 ^ [], 2810 ^ []) = relation_inverse_image(2811 ^ [], 2810 ^ []), 595 : relation(2811 ^ [])],extension(591 ^ 3,bind([[_27077, _27184, _27186, _27281], [2811 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ []), 2810 ^ [], 2809 ^ []]]))).
% 64.42/62.54 ncf('1.4.1',plain,[-(in(2809 ^ [], relation_inverse_image(2811 ^ [], 2810 ^ [])))],extension(2817 ^ 8)).
% 64.42/62.54 ncf('1.4.2',plain,[-(relation_inverse_image(2811 ^ [], 2810 ^ []) = relation_inverse_image(2811 ^ [], 2810 ^ [])), unordered_pair(relation_inverse_image(2811 ^ [], 2810 ^ []), relation_inverse_image(2811 ^ [], 2810 ^ [])) = unordered_pair(relation_inverse_image(2811 ^ [], 2810 ^ []), relation_inverse_image(2811 ^ [], 2810 ^ [])), -(relation_inverse_image(2811 ^ [], 2810 ^ []) = relation_inverse_image(2811 ^ [], 2810 ^ []))],extension(1963 ^ 6,bind([[_48034, _48036, _48038, _48040], [relation_inverse_image(2811 ^ [], 2810 ^ []), relation_inverse_image(2811 ^ [], 2810 ^ []), relation_inverse_image(2811 ^ [], 2810 ^ []), relation_inverse_image(2811 ^ [], 2810 ^ [])]]))).
% 64.42/62.54 ncf('1.4.2.1',plain,[-(unordered_pair(relation_inverse_image(2811 ^ [], 2810 ^ []), relation_inverse_image(2811 ^ [], 2810 ^ [])) = unordered_pair(relation_inverse_image(2811 ^ [], 2810 ^ []), relation_inverse_image(2811 ^ [], 2810 ^ [])))],extension(2 ^ 7,bind([[_17902], [unordered_pair(relation_inverse_image(2811 ^ [], 2810 ^ []), relation_inverse_image(2811 ^ [], 2810 ^ []))]]))).
% 64.42/62.54 ncf('1.4.2.2',plain,[relation_inverse_image(2811 ^ [], 2810 ^ []) = relation_inverse_image(2811 ^ [], 2810 ^ [])],reduction('1.4')).
% 64.42/62.54 ncf('1.4.3',plain,[-(relation(2811 ^ []))],extension(2813 ^ 4)).
% 64.42/62.54 %-----------------------------------------------------
% 64.42/62.54 End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------